LMFDB - Embedded newform 279.2.y.c.262.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,2,Mod(10,279)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("279.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			262.2
Root			$1.14660i$ of defining polynomial
Character	$\chi$	$=$	279.262
Dual form			279.2.y.c.82.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.831304 - 2.55849i) q^{2} +(-4.23677 - 3.07819i) q^{4} +(0.304192 - 0.526876i) q^{5} +(0.180508 - 1.71742i) q^{7} +(-7.04481 + 5.11835i) q^{8} +(-1.09513 - 1.21627i) q^{10} +(1.22177 - 0.543967i) q^{11} +(-3.59045 - 0.763174i) q^{13} +(-4.24394 - 1.88952i) q^{14} +(4.00227 + 12.3177i) q^{16} +(2.52396 + 1.12374i) q^{17} +(2.51157 - 0.533850i) q^{19} +(-2.91062 + 1.29589i) q^{20} +(-0.376072 - 3.57808i) q^{22} +(-0.436271 + 0.316969i) q^{23} +(2.31493 + 4.00958i) q^{25} +(-4.93733 + 8.55171i) q^{26} +(-6.05132 + 6.72067i) q^{28} +(2.51258 - 7.73291i) q^{29} +(4.75081 - 2.90341i) q^{31} +17.4262 q^{32} +(4.97326 - 5.52336i) q^{34} +(-0.849957 - 0.617530i) q^{35} +(-3.87249 - 6.70735i) q^{37} +(0.722025 - 6.86961i) q^{38} +(0.553763 + 5.26870i) q^{40} +(0.0696243 + 0.0773256i) q^{41} +(2.93904 - 0.624713i) q^{43} +(-6.85079 - 1.45618i) q^{44} +(0.448289 + 1.37969i) q^{46} +(2.07813 + 6.39584i) q^{47} +(3.93009 + 0.835366i) q^{49} +(12.1829 - 2.58955i) q^{50} +(12.8627 + 14.2855i) q^{52} +(0.292549 + 2.78341i) q^{53} +(0.0850494 - 0.809191i) q^{55} +(7.51871 + 13.0228i) q^{56} +(-17.6959 - 12.8568i) q^{58} +(-0.311970 + 0.346478i) q^{59} -5.11468 q^{61} +(-3.47898 - 14.5685i) q^{62} +(6.48190 - 19.9492i) q^{64} +(-1.49428 + 1.65957i) q^{65} +(-4.14923 + 7.18668i) q^{67} +(-7.23436 - 12.5303i) q^{68} +(-2.28652 + 1.66125i) q^{70} +(0.497420 + 4.73264i) q^{71} +(6.85725 - 3.05304i) q^{73} +(-20.3799 + 4.33188i) q^{74} +(-12.2842 - 5.46929i) q^{76} +(-0.713679 - 2.19648i) q^{77} +(-8.86044 - 3.94492i) q^{79} +(7.70738 + 1.63825i) q^{80} +(0.255716 - 0.113852i) q^{82} +(11.1642 + 12.3991i) q^{83} +(1.35984 - 0.987981i) q^{85} +(0.844916 - 8.03884i) q^{86} +(-5.82292 + 10.0856i) q^{88} +(-12.3911 - 9.00268i) q^{89} +(-1.95880 + 6.02855i) q^{91} +2.82407 q^{92} +18.0912 q^{94} +(0.482726 - 1.48568i) q^{95} +(1.03488 + 0.751881i) q^{97} +(5.40437 - 9.36065i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} - 14 q^{4} + 3 q^{5} + 2 q^{7} - 17 q^{8} - 2 q^{10} + 7 q^{11} - 7 q^{13} + 6 q^{14} - 2 q^{16} + 6 q^{17} + 16 q^{19} - 37 q^{20} + 9 q^{22} - q^{23} - 13 q^{25} - 9 q^{26} - 30 q^{28}+ \cdots + 10 q^{98}+O(q^{100}) $ 16 * q + 6 * q^2 - 14 * q^4 + 3 * q^5 + 2 * q^7 - 17 * q^8 - 2 * q^10 + 7 * q^11 - 7 * q^13 + 6 * q^14 - 2 * q^16 + 6 * q^17 + 16 * q^19 - 37 * q^20 + 9 * q^22 - q^23 - 13 * q^25 - 9 * q^26 - 30 * q^28 + 14 * q^29 + 15 * q^31 + 42 * q^32 - 32 * q^34 + 9 * q^35 - 8 * q^37 - 8 * q^38 - q^40 + 8 * q^41 + 23 * q^43 - 39 * q^44 + 34 * q^46 - 14 * q^47 + 2 * q^49 - 3 * q^50 + 29 * q^52 - 6 * q^53 - 7 * q^55 + 30 * q^56 - 15 * q^58 - 4 * q^59 - 60 * q^61 + 25 * q^62 + 23 * q^64 + 12 * q^65 + 13 * q^67 - 30 * q^68 + 12 * q^70 + 14 * q^71 + 2 * q^73 - 13 * q^74 - 12 * q^76 - 18 * q^77 + 18 * q^79 - 36 * q^80 + 14 * q^82 + 16 * q^83 + 37 * q^85 + 26 * q^86 - 17 * q^88 - q^89 + 8 * q^91 + 64 * q^92 + 44 * q^94 + 22 * q^95 + 3 * q^97 + 10 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{11}{15}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.831304	−	2.55849i	0.587821	−	1.80913i	0.000184800	−	1.00000i	$-0.499941\pi$
$2$	0.831304	−	2.55849i	0.587821	−	1.80913i	0.587636	−	0.809126i	$-0.300059\pi$
$3$		0			0
$3$		0			0
$4$	−4.23677	−	3.07819i	−2.11839	−	1.53910i
$5$	0.304192	−	0.526876i	0.136039	−	0.235626i	−0.789955	−	0.613165i	$-0.789896\pi$
$5$	0.304192	−	0.526876i	0.136039	−	0.235626i	0.925994	+	0.377539i	$0.123230\pi$
$6$		0			0
$7$	0.180508	−	1.71742i	0.0682256	−	0.649123i	−0.905958	−	0.423367i	$-0.860848\pi$
$7$	0.180508	−	1.71742i	0.0682256	−	0.649123i	0.974184	−	0.225756i	$-0.0724853\pi$
$8$	−7.04481	+	5.11835i	−2.49072	+	1.80961i
$9$		0			0
$10$	−1.09513	−	1.21627i	−0.346311	−	0.384617i
$11$	1.22177	−	0.543967i	0.368377	−	0.164012i	−0.214195	−	0.976791i	$-0.568713\pi$
$11$	1.22177	−	0.543967i	0.368377	−	0.164012i	0.582572	+	0.812779i	$0.302046\pi$
$12$		0			0
$13$	−3.59045	−	0.763174i	−0.995812	−	0.211666i	−0.318946	−	0.947773i	$-0.603329\pi$
$13$	−3.59045	−	0.763174i	−0.995812	−	0.211666i	−0.676866	+	0.736106i	$0.736662\pi$
$14$	−4.24394	−	1.88952i	−1.13424	−	0.504997i
$15$		0			0
$16$	4.00227	+	12.3177i	1.00057	+	3.07943i
$17$	2.52396	+	1.12374i	0.612150	+	0.272547i	0.689304	−	0.724472i	$-0.257916\pi$
$17$	2.52396	+	1.12374i	0.612150	+	0.272547i	−0.0771534	+	0.997019i	$0.524583\pi$
$18$		0			0
$19$	2.51157	−	0.533850i	0.576193	−	0.122474i	0.0894075	−	0.995995i	$-0.471503\pi$
$19$	2.51157	−	0.533850i	0.576193	−	0.122474i	0.486786	+	0.873522i	$0.338169\pi$
$20$	−2.91062	+	1.29589i	−0.650834	+	0.289770i
$21$		0			0
$22$	−0.376072	−	3.57808i	−0.0801788	−	0.762850i
$23$	−0.436271	+	0.316969i	−0.0909688	+	0.0660927i	−0.632340	−	0.774691i	$-0.717905\pi$
$23$	−0.436271	+	0.316969i	−0.0909688	+	0.0660927i	0.541371	+	0.840784i	$0.317905\pi$
$24$		0			0
$25$	2.31493	+	4.00958i	0.462987	+	0.801917i
$26$	−4.93733	+	8.55171i	−0.968290	+	1.67713i
$27$		0			0
$28$	−6.05132	+	6.72067i	−1.14359	+	1.27009i
$29$	2.51258	−	7.73291i	0.466574	−	1.43597i	−0.390419	−	0.920637i	$-0.627670\pi$
$29$	2.51258	−	7.73291i	0.466574	−	1.43597i	0.856993	−	0.515329i	$-0.172330\pi$
$30$		0			0
$31$	4.75081	−	2.90341i	0.853271	−	0.521468i
$31$	4.75081	−	2.90341i	0.853271	−	0.521468i
$32$	17.4262			3.08054
$33$		0			0
$34$	4.97326	−	5.52336i	0.852906	−	0.947248i
$35$	−0.849957	−	0.617530i	−0.143669	−	0.104382i
$36$		0			0
$37$	−3.87249	−	6.70735i	−0.636633	−	1.10268i	−0.986167	−	0.165757i	$-0.946993\pi$
$37$	−3.87249	−	6.70735i	−0.636633	−	1.10268i	0.349533	−	0.936924i	$-0.386340\pi$
$38$	0.722025	−	6.86961i	0.117128	−	1.11440i
$39$		0			0
$40$	0.553763	+	5.26870i	0.0875576	+	0.833055i
$41$	0.0696243	+	0.0773256i	0.0108735	+	0.0120762i	0.748557	−	0.663070i	$-0.230747\pi$
$41$	0.0696243	+	0.0773256i	0.0108735	+	0.0120762i	−0.737684	+	0.675147i	$0.764080\pi$
$42$		0			0
$43$	2.93904	−	0.624713i	0.448200	−	0.0952678i	0.0217184	−	0.999764i	$-0.493086\pi$
$43$	2.93904	−	0.624713i	0.448200	−	0.0952678i	0.426481	+	0.904496i	$0.359753\pi$
$44$	−6.85079	−	1.45618i	−1.03280	−	0.219527i
$45$		0			0
$46$	0.448289	+	1.37969i	0.0660967	+	0.203425i
$47$	2.07813	+	6.39584i	0.303127	+	0.932929i	0.980370	+	0.197169i	$0.0631747\pi$
$47$	2.07813	+	6.39584i	0.303127	+	0.932929i	−0.677243	+	0.735760i	$0.736825\pi$
$48$		0			0
$49$	3.93009	+	0.835366i	0.561441	+	0.119338i
$50$	12.1829	−	2.58955i	1.72292	−	0.366218i
$51$		0			0
$52$	12.8627	+	14.2855i	1.78374	+	1.98104i
$53$	0.292549	+	2.78341i	0.0401846	+	0.382331i	0.996068	+	0.0885864i	$0.0282349\pi$
$53$	0.292549	+	2.78341i	0.0401846	+	0.382331i	−0.955884	+	0.293745i	$0.905098\pi$
$54$		0			0
$55$	0.0850494	−	0.809191i	0.0114681	−	0.109111i
$56$	7.51871	+	13.0228i	1.00473	+	1.74024i
$57$		0			0
$58$	−17.6959	−	12.8568i	−2.32358	−	1.68818i
$59$	−0.311970	+	0.346478i	−0.0406151	+	0.0451076i	−0.763110	−	0.646269i	$-0.776329\pi$
$59$	−0.311970	+	0.346478i	−0.0406151	+	0.0451076i	0.722495	+	0.691376i	$0.242995\pi$
$60$		0			0
$61$	−5.11468			−0.654867			−0.327434	−	0.944874i	$-0.606184\pi$
$61$	−5.11468			−0.654867			−0.327434	+	0.944874i	$0.606184\pi$
$62$	−3.47898	−	14.5685i	−0.441831	−	1.85020i
$63$		0			0
$64$	6.48190	−	19.9492i	0.810238	−	2.49365i
$65$	−1.49428	+	1.65957i	−0.185343	+	0.205844i
$66$		0			0
$67$	−4.14923	+	7.18668i	−0.506910	+	0.877993i	0.493058	+	0.869996i	$0.335879\pi$
$67$	−4.14923	+	7.18668i	−0.506910	+	0.877993i	−0.999968	+	0.00799701i	$0.997454\pi$
$68$	−7.23436	−	12.5303i	−0.877294	−	1.51952i
$69$		0			0
$70$	−2.28652	+	1.66125i	−0.273291	+	0.198558i
$71$	0.497420	+	4.73264i	0.0590329	+	0.561661i	0.983565	+	0.180556i	$0.0577897\pi$
$71$	0.497420	+	4.73264i	0.0590329	+	0.561661i	−0.924532	+	0.381105i	$0.875544\pi$
$72$		0			0
$73$	6.85725	−	3.05304i	0.802580	−	0.357332i	0.0358953	−	0.999356i	$-0.488572\pi$
$73$	6.85725	−	3.05304i	0.802580	−	0.357332i	0.766685	+	0.642024i	$0.221905\pi$
$74$	−20.3799	+	4.33188i	−2.36911	+	0.503571i
$75$		0			0
$76$	−12.2842	−	5.46929i	−1.40910	−	0.627371i
$77$	−0.713679	−	2.19648i	−0.0813313	−	0.250312i
$78$		0			0
$79$	−8.86044	−	3.94492i	−0.996877	−	0.443838i	−0.157577	−	0.987507i	$-0.550368\pi$
$79$	−8.86044	−	3.94492i	−0.996877	−	0.443838i	−0.839300	+	0.543668i	$0.817035\pi$
$80$	7.70738	+	1.63825i	0.861711	+	0.183162i
$81$		0			0
$82$	0.255716	−	0.113852i	0.0282391	−	0.0125728i
$83$	11.1642	+	12.3991i	1.22543	+	1.36097i	0.911380	+	0.411567i	$0.135018\pi$
$83$	11.1642	+	12.3991i	1.22543	+	1.36097i	0.314047	+	0.949407i	$0.398315\pi$
$84$		0			0
$85$	1.35984	−	0.987981i	0.147495	−	0.107162i
$86$	0.844916	−	8.03884i	0.0911096	−	0.866850i
$87$		0			0
$88$	−5.82292	+	10.0856i	−0.620725	+	1.07513i
$89$	−12.3911	−	9.00268i	−1.31346	−	0.954282i	−0.999989	−	0.00468333i	$-0.998509\pi$
$89$	−12.3911	−	9.00268i	−1.31346	−	0.954282i	−0.313468	−	0.949599i	$-0.601491\pi$
$90$		0			0
$91$	−1.95880	+	6.02855i	−0.205338	+	0.631964i
$92$	2.82407			0.294430
$93$		0			0
$94$	18.0912			1.86597
$95$	0.482726	−	1.48568i	0.0495266	−	0.152427i
$96$		0			0
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	0.639082	−	0.769138i	$-0.279314\pi$
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	−0.534007	+	0.845480i	$0.679314\pi$
$98$	5.40437	−	9.36065i	0.545924	−	0.945568i
$99$		0			0
$100$	2.53443	−	24.1135i	0.253443	−	2.41135i
$101$	6.56941	−	4.77296i	0.653681	−	0.474927i	−0.210842	−	0.977520i	$-0.567621\pi$
$101$	6.56941	−	4.77296i	0.653681	−	0.474927i	0.864523	+	0.502593i	$0.167621\pi$
$102$		0			0
$103$	10.1390	+	11.2605i	0.999026	+	1.10953i	0.993982	+	0.109544i	$0.0349389\pi$
$103$	10.1390	+	11.2605i	0.999026	+	1.10953i	0.00504416	+	0.999987i	$0.498394\pi$
$104$	29.2002	−	13.0008i	2.86332	−	1.27483i
$105$		0			0
$106$	7.36453	+	1.56538i	0.715307	+	0.152043i
$107$	11.3057	+	5.03362i	1.09296	+	0.486618i	0.872419	−	0.488759i	$-0.162550\pi$
$107$	11.3057	+	5.03362i	1.09296	+	0.486618i	0.220543	+	0.975377i	$0.429217\pi$
$108$		0			0
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	0.999264	+	0.0383645i	$0.0122148\pi$
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	−0.785871	+	0.618390i	$0.787785\pi$
$110$	−1.99960	−	0.890281i	−0.190655	−	0.0848850i
$111$		0			0
$112$	21.8772	−	4.65013i	2.06720	−	0.439396i
$113$	−15.2304	+	6.78103i	−1.43276	+	0.637906i	−0.968776	−	0.247938i	$-0.920247\pi$
$113$	−15.2304	+	6.78103i	−1.43276	+	0.637906i	−0.463984	+	0.885844i	$0.653580\pi$
$114$		0			0
$115$	0.0342934	+	0.326280i	0.00319788	+	0.0304258i
$116$	−34.4486	+	25.0284i	−3.19847	+	2.32383i
$117$		0			0
$118$	0.627119	+	1.08620i	0.0577310	+	0.0999930i
$119$	2.38553	−	4.13185i	0.218681	−	0.378767i
$120$		0			0
$121$	−6.16362	+	6.84539i	−0.560329	+	0.622308i
$122$	−4.25185	+	13.0859i	−0.384944	+	1.18474i
$123$		0			0
$124$	−29.0654	−	2.32284i	−2.61015	−	0.208597i
$125$	5.85866			0.524014
$126$		0			0
$127$	−8.63810	+	9.59358i	−0.766507	+	0.851293i	−0.992425	−	0.122854i	$-0.960795\pi$
$127$	−8.63810	+	9.59358i	−0.766507	+	0.851293i	0.225918	+	0.974146i	$0.427462\pi$
$128$	−17.4553	−	12.6820i	−1.54285	−	1.12095i
$129$		0			0
$130$	3.00379	+	5.20272i	0.263450	+	0.456309i
$131$	−0.254818	+	2.42443i	−0.0222635	+	0.211823i	0.977735	+	0.209846i	$0.0672962\pi$
$131$	−0.254818	+	2.42443i	−0.0222635	+	0.211823i	−0.999998	+	0.00197767i	$0.999370\pi$
$132$		0			0
$133$	−0.463486	−	4.40978i	−0.0401894	−	0.382376i
$134$	14.9378	+	16.5901i	1.29043	+	1.43317i
$135$		0			0
$136$	−23.5325	+	5.00199i	−2.01790	+	0.428917i
$137$	7.96586	+	1.69320i	0.680570	+	0.144660i	0.535210	−	0.844719i	$-0.320233\pi$
$137$	7.96586	+	1.69320i	0.680570	+	0.144660i	0.145360	+	0.989379i	$0.453566\pi$
$138$		0			0
$139$	−0.418212	−	1.28712i	−0.0354723	−	0.109172i	0.931753	−	0.363094i	$-0.118280\pi$
$139$	−0.418212	−	1.28712i	−0.0354723	−	0.109172i	−0.967225	+	0.253921i	$0.918280\pi$
$140$	1.70020	+	5.23267i	0.143693	+	0.442241i
$141$		0			0
$142$	12.5219	+	2.66162i	1.05082	+	0.223358i
$143$	−4.80184	+	1.02066i	−0.401550	+	0.0853522i
$144$		0			0
$145$	−3.30998	−	3.67611i	−0.274879	−	0.305284i
$146$	−2.11072	−	20.0822i	−0.174685	−	1.66201i
$147$		0			0
$148$	−4.23967	+	40.3378i	−0.348499	+	3.31574i
$149$	−4.50192	−	7.79756i	−0.368812	−	0.638801i	0.620568	−	0.784153i	$-0.286902\pi$
$149$	−4.50192	−	7.79756i	−0.368812	−	0.638801i	−0.989380	+	0.145351i	$0.953569\pi$
$150$		0			0
$151$	2.59566	+	1.88585i	0.211232	+	0.153469i	0.688371	−	0.725359i	$-0.258326\pi$
$151$	2.59566	+	1.88585i	0.211232	+	0.153469i	−0.477139	+	0.878828i	$0.658326\pi$
$152$	−14.9611	+	16.6160i	−1.21350	+	1.34773i
$153$		0			0
$154$	−6.21295			−0.500654
$155$	−0.0845781	−	3.38628i	−0.00679348	−	0.271993i
$156$		0			0
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	−0.983662	−	0.180027i	$-0.942382\pi$
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	0.901616	+	0.432537i	$0.142382\pi$
$158$	−17.4588	+	19.3899i	−1.38894	+	1.54258i
$159$		0			0
$160$	5.30090	−	9.18143i	0.419073	−	0.725856i
$161$	0.465619	+	0.806476i	0.0366959	+	0.0635592i
$162$		0			0
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	−0.641559	−	0.767074i	$-0.721712\pi$
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	0.531278	+	0.847198i	$0.321712\pi$
$164$	−0.0569589	−	0.541928i	−0.00444774	−	0.0423175i
$165$		0			0
$166$	41.0037	−	18.2560i	3.18250	−	1.41694i
$167$	−13.7102	+	2.91419i	−1.06093	+	0.225507i	−0.705145	−	0.709063i	$-0.749118\pi$
$167$	−13.7102	+	2.91419i	−1.06093	+	0.225507i	−0.355780	+	0.934570i	$0.615785\pi$
$168$		0			0
$169$	0.432821	+	0.192704i	0.0332939	+	0.0148234i
$170$	−1.39730	−	4.30045i	−0.107168	−	0.329829i
$171$		0			0
$172$	−14.3750	−	6.40018i	−1.09609	−	0.488009i
$173$	−0.0117191	−	0.00249097i	−0.000890985	−	0.000189385i	0.207466	−	0.978242i	$-0.433478\pi$
$173$	−0.0117191	−	0.00249097i	−0.000890985	−	0.000189385i	−0.208357	+	0.978053i	$0.566812\pi$
$174$		0			0
$175$	7.30400	−	3.25195i	0.552131	−	0.245824i
$176$	11.5903	+	12.8723i	0.873651	+	0.970288i
$177$		0			0
$178$	−33.3341	+	24.2186i	−2.49849	+	1.81526i
$179$	−1.04299	+	9.92334i	−0.0779564	+	0.741706i	0.883812	+	0.467842i	$0.154968\pi$
$179$	−1.04299	+	9.92334i	−0.0779564	+	0.741706i	−0.961769	+	0.273864i	$0.911698\pi$
$180$		0			0
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	−0.280004	−	0.959999i	$-0.590336\pi$
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	0.971385	−	0.237509i	$-0.0763308\pi$
$182$	13.7956	+	10.0231i	1.02260	+	0.742963i
$183$		0			0
$184$	1.45108	−	4.46598i	0.106975	−	0.329236i
$185$	−4.71192			−0.346427
$186$		0			0
$187$	3.69497			0.270203
$188$	10.8831	−	33.4946i	0.793728	−	2.44284i
$189$		0			0
$190$	−3.39980	−	2.47010i	−0.246647	−	0.179200i
$191$	0.599059	−	1.03760i	0.0433464	−	0.0750782i	−0.843538	−	0.537069i	$-0.819531\pi$
$191$	0.599059	−	1.03760i	0.0433464	−	0.0750782i	0.886885	+	0.461991i	$0.152865\pi$
$192$		0			0
$193$	−1.33029	+	12.6568i	−0.0957562	+	0.911059i	0.836184	+	0.548448i	$0.184781\pi$
$193$	−1.33029	+	12.6568i	−0.0957562	+	0.911059i	−0.931941	+	0.362611i	$0.881885\pi$
$194$	2.78398	−	2.02268i	0.199878	−	0.145220i
$195$		0			0
$196$	−14.0795	−	15.6368i	−1.00568	−	1.11692i
$197$	2.71195	−	1.20744i	0.193218	−	0.0860263i	−0.307847	−	0.951436i	$-0.599608\pi$
$197$	2.71195	−	1.20744i	0.193218	−	0.0860263i	0.501065	+	0.865410i	$0.332942\pi$
$198$		0			0
$199$	12.8960	+	2.74112i	0.914170	+	0.194313i	0.640900	−	0.767625i	$-0.278561\pi$
$199$	12.8960	+	2.74112i	0.914170	+	0.194313i	0.273270	+	0.961937i	$0.411895\pi$
$200$	−36.8307	−	16.3981i	−2.60433	−	1.15952i
$201$		0			0
$202$	−6.75039	−	20.7755i	−0.474955	−	1.46176i
$203$	−12.8271	−	5.71100i	−0.900287	−	0.400834i
$204$		0			0
$205$	0.0619201	−	0.0131615i	0.00432469	−	0.000919241i
$206$	37.2385	−	16.5796i	2.59453	−	1.15516i
$207$		0			0
$208$	−4.96940	−	47.2807i	−0.344566	−	3.27832i
$209$	2.77816	−	2.01845i	0.192169	−	0.139619i
$210$		0			0
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	−0.987343	−	0.158600i	$-0.949302\pi$
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	0.356320	−	0.934364i	$-0.384031\pi$
$212$	7.32843	−	12.6932i	0.503318	−	0.871773i
$213$		0			0
$214$	22.2769	−	24.7410i	1.52282	−	1.69126i
$215$	0.564887	−	1.73854i	0.0385250	−	0.118568i
$216$		0			0
$217$	−4.12881	−	8.68322i	−0.280282	−	0.589456i
$218$	19.3949			1.31359
$219$		0			0
$220$	−2.85118	+	3.16656i	−0.192227	+	0.213489i
$221$	−8.20455	−	5.96096i	−0.551898	−	0.400977i
$222$		0			0
$223$	−4.69801	−	8.13718i	−0.314602	−	0.544906i	0.664751	−	0.747065i	$-0.268538\pi$
$223$	−4.69801	−	8.13718i	−0.314602	−	0.544906i	−0.979353	+	0.202159i	$0.935204\pi$
$224$	3.14557	−	29.9281i	0.210172	−	1.99965i
$225$		0			0
$226$	4.68807	+	44.6040i	0.311846	+	2.96702i
$227$	−5.66046	−	6.28658i	−0.375698	−	0.417255i	0.525410	−	0.850849i	$-0.323912\pi$
$227$	−5.66046	−	6.28658i	−0.375698	−	0.417255i	−0.901108	+	0.433594i	$0.857245\pi$
$228$		0			0
$229$	−22.3443	+	4.74942i	−1.47655	+	0.313850i	−0.874663	−	0.484731i	$-0.838917\pi$
$229$	−22.3443	+	4.74942i	−1.47655	+	0.313850i	−0.601887	+	0.798582i	$0.705584\pi$
$230$	0.863293	+	0.183499i	0.0569238	+	0.0120995i
$231$		0			0
$232$	21.8792	+	67.3372i	1.43644	+	4.42090i
$233$	−5.02260	−	15.4580i	−0.329042	−	1.01269i	−0.969583	−	0.244762i	$-0.921290\pi$
$233$	−5.02260	−	15.4580i	−0.329042	−	1.01269i	0.640542	−	0.767923i	$-0.278710\pi$
$234$		0			0
$235$	4.00196	+	0.850643i	0.261059	+	0.0554899i
$236$	2.38828	−	0.507644i	0.155463	−	0.0330448i
$237$		0			0
$238$	−8.58821	−	9.53817i	−0.556691	−	0.618268i
$239$	1.91005	+	18.1729i	0.123551	+	1.17551i	0.864035	+	0.503433i	$0.167930\pi$
$239$	1.91005	+	18.1729i	0.123551	+	1.17551i	−0.740484	+	0.672074i	$0.765404\pi$
$240$		0			0
$241$	1.89944	−	18.0720i	0.122354	−	1.16412i	−0.745222	−	0.666816i	$-0.767657\pi$
$241$	1.89944	−	18.0720i	0.122354	−	1.16412i	0.867576	−	0.497304i	$-0.165677\pi$
$242$	12.3900	+	21.4602i	0.796461	+	1.37951i
$243$		0			0
$244$	21.6697	+	15.7440i	1.38726	+	1.00790i
$245$	1.63564	−	1.81656i	0.104497	−	0.116056i
$246$		0			0
$247$	−9.42508			−0.599704
$248$	−18.6079	+	44.7703i	−1.18160	+	2.84292i
$249$		0			0
$250$	4.87032	−	14.9893i	0.308026	−	0.948007i
$251$	15.3433	−	17.0405i	0.968461	−	1.07558i	−0.0286471	−	0.999590i	$-0.509120\pi$
$251$	15.3433	−	17.0405i	0.968461	−	1.07558i	0.997108	−	0.0759953i	$-0.0242134\pi$
$252$		0			0
$253$	−0.360602	+	0.624580i	−0.0226708	+	0.0392670i
$254$	17.3642	+	30.0757i	1.08953	+	1.88712i
$255$		0			0
$256$	−13.0179	+	9.45807i	−0.813620	+	0.591129i
$257$	0.0111002	+	0.105611i	0.000692411	+	0.00658785i	0.994863	−	0.101234i	$-0.0322791\pi$
$257$	0.0111002	+	0.105611i	0.000692411	+	0.00658785i	−0.994170	+	0.107822i	$0.965612\pi$
$258$		0			0
$259$	−12.2183	+	5.43996i	−0.759211	+	0.338022i
$260$	11.4394	−	2.43152i	0.709443	−	0.150797i
$261$		0			0
$262$	5.99105	+	2.66739i	0.370128	+	0.164792i
$263$	2.25499	+	6.94015i	0.139049	+	0.427948i	0.996198	−	0.0871204i	$-0.0277665\pi$
$263$	2.25499	+	6.94015i	0.139049	+	0.427948i	−0.857149	+	0.515068i	$0.827766\pi$
$264$		0			0
$265$	1.55550	+	0.692555i	0.0955539	+	0.0425433i
$266$	−11.6677	−	2.48004i	−0.715391	−	0.152061i
$267$		0			0
$268$	39.7014	−	17.6762i	2.42515	−	1.07974i
$269$	−10.8529	−	12.0533i	−0.661711	−	0.734905i	0.315088	−	0.949063i	$-0.397966\pi$
$269$	−10.8529	−	12.0533i	−0.661711	−	0.734905i	−0.976799	+	0.214158i	$0.931299\pi$
$270$		0			0
$271$	4.16291	−	3.02453i	0.252879	−	0.183727i	−0.454123	−	0.890939i	$-0.650047\pi$
$271$	4.16291	−	3.02453i	0.252879	−	0.183727i	0.707002	+	0.707212i	$0.250047\pi$
$272$	−3.74034	+	35.5870i	−0.226792	+	2.15778i
$273$		0			0
$274$	10.9541	−	18.9730i	0.661760	−	1.14620i
$275$	5.00939	+	3.63954i	0.302078	+	0.219472i
$276$		0			0
$277$	−5.22944	+	16.0946i	−0.314207	+	0.967029i	0.661873	+	0.749616i	$0.269762\pi$
$277$	−5.22944	+	16.0946i	−0.314207	+	0.967029i	−0.976080	+	0.217413i	$0.930238\pi$
$278$	−3.64076			−0.218358
$279$		0			0
$280$	9.14853			0.546729
$281$	−0.589193	+	1.81335i	−0.0351483	+	0.108175i	−0.967091	−	0.254429i	$-0.918112\pi$
$281$	−0.589193	+	1.81335i	−0.0351483	+	0.108175i	0.931943	+	0.362605i	$0.118112\pi$
$282$		0			0
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	0.891539	−	0.452944i	$-0.149626\pi$
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	−0.155274	+	0.987871i	$0.549626\pi$
$284$	12.4605	−	21.5823i	0.739396	−	1.28067i
$285$		0			0
$286$	−1.38043	+	13.1339i	−0.0816268	+	0.776627i
$287$	0.145368	−	0.105616i	0.00858081	−	0.00623433i
$288$		0			0
$289$	−6.26763	−	6.96091i	−0.368684	−	0.409465i
$290$	−12.1569	+	5.41259i	−0.713876	+	0.317838i
$291$		0			0
$292$	−38.4504	−	8.17289i	−2.25014	−	0.478282i
$293$	−24.4772	−	10.8980i	−1.42998	−	0.636666i	−0.461810	−	0.886979i	$-0.652800\pi$
$293$	−24.4772	−	10.8980i	−1.42998	−	0.636666i	−0.968165	+	0.250313i	$0.919467\pi$
$294$		0			0
$295$	0.0876522	+	0.269766i	0.00510331	+	0.0157064i
$296$	61.6115	+	27.4312i	3.58110	+	1.59441i
$297$		0			0
$298$	−23.6924	+	5.03599i	−1.37247	+	0.291727i
$299$	1.80831	−	0.805113i	0.104577	−	0.0465609i
$300$		0			0
$301$	−0.542373	−	5.16033i	−0.0312619	−	0.297437i
$302$	6.98272	−	5.07324i	0.401810	−	0.291932i
$303$		0			0
$304$	16.6278	+	28.8002i	0.953670	+	1.65181i
$305$	−1.55584	+	2.69480i	−0.0890873	+	0.154304i
$306$		0			0
$307$	5.98956	−	6.65208i	0.341842	−	0.379654i	−0.547570	−	0.836760i	$-0.684447\pi$
$307$	5.98956	−	6.65208i	0.341842	−	0.379654i	0.889413	+	0.457105i	$0.151114\pi$
$308$	−3.73749	+	11.5028i	−0.212963	+	0.655434i
$309$		0			0
$310$	−8.73408	−	2.59864i	−0.496062	−	0.147593i
$311$	−20.6556			−1.17127			−0.585637	−	0.810574i	$-0.699156\pi$
$311$	−20.6556			−1.17127			−0.585637	+	0.810574i	$0.699156\pi$
$312$		0			0
$313$	0.301993	−	0.335397i	0.0170696	−	0.0189577i	−0.734550	−	0.678555i	$-0.762606\pi$
$313$	0.301993	−	0.335397i	0.0170696	−	0.0189577i	0.751619	+	0.659597i	$0.229273\pi$
$314$	7.24032	+	5.26040i	0.408595	+	0.296862i
$315$		0			0
$316$	25.3964	+	43.9879i	1.42866	+	2.47451i
$317$	−0.583357	+	5.55027i	−0.0327646	+	0.311734i	0.965849	+	0.259104i	$0.0834272\pi$
$317$	−0.583357	+	5.55027i	−0.0327646	+	0.311734i	−0.998614	+	0.0526304i	$0.983239\pi$
$318$		0			0
$319$	−1.13666	−	10.8146i	−0.0636407	−	0.605501i
$320$	−8.53903	−	9.48355i	−0.477346	−	0.530147i
$321$		0			0
$322$	2.45043	−	0.520855i	0.136557	−	0.0290261i
$323$	6.93901	+	1.47493i	0.386097	+	0.0820674i
$324$		0			0
$325$	−5.25165	−	16.1629i	−0.291309	−	0.896557i
$326$	1.44676	+	4.45266i	0.0801284	+	0.246610i
$327$		0			0
$328$	−0.886270	−	0.188382i	−0.0489360	−	0.0104017i
$329$	11.3595	−	2.41453i	0.626267	−	0.133117i
$330$		0			0
$331$	16.1966	+	17.9882i	0.890246	+	0.988719i	0.999986	−	0.00524168i	$-0.00166849\pi$
$331$	16.1966	+	17.9882i	0.890246	+	0.988719i	−0.109740	+	0.993960i	$0.535002\pi$
$332$	−9.13329	−	86.8975i	−0.501255	−	4.76912i
$333$		0			0
$334$	−3.94140	+	37.4999i	−0.215664	+	2.05191i
$335$	2.52433	+	4.37226i	0.137919	+	0.238882i
$336$		0			0
$337$	−8.92830	−	6.48679i	−0.486355	−	0.353358i	0.317426	−	0.948283i	$-0.397182\pi$
$337$	−8.92830	−	6.48679i	−0.486355	−	0.353358i	−0.803781	+	0.594925i	$0.797182\pi$
$338$	0.852838	−	0.947173i	0.0463883	−	0.0515194i
$339$		0			0
$340$	−8.80253			−0.477384
$341$	4.22504	−	6.13158i	0.228799	−	0.332044i
$342$		0			0
$343$	5.87953	−	18.0953i	0.317465	−	0.977056i
$344$	−17.5075	+	19.4440i	−0.943941	+	1.04835i
$345$		0			0
$346$	−0.0161152	+	0.0279124i	−0.000866360	+	0.00150058i
$347$	−9.28369	−	16.0798i	−0.498375	−	0.863210i	0.501624	−	0.865086i	$-0.332736\pi$
$347$	−9.28369	−	16.0798i	−0.498375	−	0.863210i	−0.999998	+	0.00187589i	$0.999403\pi$
$348$		0			0
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.397855	−	0.917448i	$-0.369755\pi$
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.995489	−	0.0948756i	$-0.0302453\pi$
$350$	−2.24824	−	21.3906i	−0.120173	−	1.14337i
$351$		0			0
$352$	21.2908	−	9.47926i	1.13480	−	0.505246i
$353$	31.5094	−	6.69754i	1.67708	−	0.356474i	0.731493	−	0.681849i	$-0.238824\pi$
$353$	31.5094	−	6.69754i	1.67708	−	0.356474i	0.945585	+	0.325375i	$0.105490\pi$
$354$		0			0
$355$	2.64482	+	1.17755i	0.140373	+	0.0624980i
$356$	24.7864	+	76.2846i	1.31367	+	4.04307i
$357$		0			0
$358$	24.5217	+	10.9178i	1.29601	+	0.577023i
$359$	20.6998	+	4.39988i	1.09249	+	0.232217i	0.718718	−	0.695302i	$-0.244729\pi$
$359$	20.6998	+	4.39988i	1.09249	+	0.232217i	0.373777	+	0.927519i	$0.378063\pi$
$360$		0			0
$361$	−11.3344	+	5.04639i	−0.596547	+	0.265600i
$362$	−33.4869	−	37.1910i	−1.76003	−	1.95472i
$363$		0			0
$364$	26.8560	−	19.5120i	1.40764	−	1.02271i
$365$	0.477344	−	4.54163i	0.0249853	−	0.237720i
$366$		0			0
$367$	−6.49822	+	11.2552i	−0.339204	+	0.587519i	−0.984283	−	0.176597i	$-0.943491\pi$
$367$	−6.49822	+	11.2552i	−0.339204	+	0.587519i	0.645079	+	0.764116i	$0.276824\pi$
$368$	−5.65042	−	4.10527i	−0.294549	−	0.214002i
$369$		0			0
$370$	−3.91704	+	12.0554i	−0.203637	+	0.626730i
$371$	4.83309			0.250922
$372$		0			0
$373$	−4.42592			−0.229166			−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592			−0.229166			−0.114583	+	0.993414i	$0.536553\pi$
$374$	3.07165	−	9.45355i	0.158831	−	0.488832i
$375$		0			0
$376$	−47.3762	−	34.4208i	−2.44324	−	1.77512i
$377$	−14.9228	+	25.8471i	−0.768566	+	1.33119i
$378$		0			0
$379$	1.56330	−	14.8738i	0.0803013	−	0.764016i	−0.878078	−	0.478518i	$-0.841174\pi$
$379$	1.56330	−	14.8738i	0.0803013	−	0.764016i	0.958379	−	0.285498i	$-0.0921591\pi$
$380$	−6.61840	+	4.80855i	−0.339517	+	0.246673i
$381$		0			0
$382$	−2.15669	−	2.39525i	−0.110346	−	0.122552i
$383$	10.6431	−	4.73862i	0.543838	−	0.242132i	−0.116382	−	0.993205i	$-0.537130\pi$
$383$	10.6431	−	4.73862i	0.543838	−	0.242132i	0.660220	+	0.751072i	$0.270463\pi$
$384$		0			0
$385$	−1.37437	−	0.292131i	−0.0700442	−	0.0148884i
$386$	31.2765	+	13.9252i	1.59193	+	0.708774i
$387$		0			0
$388$	−2.07009	−	6.37110i	−0.105093	−	0.323443i
$389$	−13.1568	−	5.85779i	−0.667077	−	0.297002i	0.0451198	−	0.998982i	$-0.485633\pi$
$389$	−13.1568	−	5.85779i	−0.667077	−	0.297002i	−0.712197	+	0.701980i	$0.752300\pi$
$390$		0			0
$391$	−1.45732	+	0.309763i	−0.0737000	+	0.0156654i
$392$	−31.9624	+	14.2306i	−1.61435	+	0.718753i
$393$		0			0
$394$	−0.834763	−	7.94224i	−0.0420547	−	0.400124i
$395$	−4.77376	+	3.46834i	−0.240194	+	0.174511i
$396$		0			0
$397$	−7.89506	−	13.6746i	−0.396242	−	0.686311i	0.597017	−	0.802229i	$-0.296352\pi$
$397$	−7.89506	−	13.6746i	−0.396242	−	0.686311i	−0.993259	+	0.115918i	$0.963019\pi$
$398$	17.7336	−	30.7155i	0.888904	−	1.53963i
$399$		0			0
$400$	−40.1240	+	44.5622i	−2.00620	+	2.22811i
$401$	−9.58670	+	29.5048i	−0.478737	+	1.47340i	0.362114	+	0.932134i	$0.382055\pi$
$401$	−9.58670	+	29.5048i	−0.478737	+	1.47340i	−0.840851	+	0.541267i	$0.817945\pi$
$402$		0			0
$403$	−19.2734	+	6.79886i	−0.960075	+	0.338675i
$404$	−42.5252			−2.11571
$405$		0			0
$406$	−25.2748	+	28.0705i	−1.25437	+	1.39311i
$407$	−8.37986	−	6.08832i	−0.415374	−	0.301787i
$408$		0			0
$409$	−3.29291	−	5.70349i	−0.162824	−	0.282019i	0.773056	−	0.634337i	$-0.218727\pi$
$409$	−3.29291	−	5.70349i	−0.162824	−	0.282019i	−0.935880	+	0.352318i	$0.885394\pi$
$410$	0.0178008	−	0.169363i	0.000879119	−	0.00836425i
$411$		0			0
$412$	−8.29462	−	78.9180i	−0.408647	−	3.88801i
$413$	0.538735	+	0.598326i	0.0265094	+	0.0294417i
$414$		0			0
$415$	9.92882	−	2.11043i	0.487386	−	0.103597i
$416$	−62.5679	−	13.2992i	−3.06764	−	0.652047i
$417$		0			0
$418$	−2.85469	−	8.78583i	−0.139627	−	0.429729i
$419$	4.53389	+	13.9539i	0.221495	+	0.681692i	0.998628	+	0.0523559i	$0.0166730\pi$
$419$	4.53389	+	13.9539i	0.221495	+	0.681692i	−0.777133	+	0.629336i	$0.783327\pi$
$420$		0			0
$421$	26.1321	+	5.55454i	1.27360	+	0.270712i	0.794616	−	0.607112i	$-0.207672\pi$
$421$	26.1321	+	5.55454i	1.27360	+	0.270712i	0.478983	+	0.877824i	$0.341006\pi$
$422$	−48.2390	+	10.2535i	−2.34824	+	0.499133i
$423$		0			0
$424$	−16.3074	−	18.1113i	−0.791959	−	0.879560i
$425$	1.33708	+	12.7214i	0.0648577	+	0.617079i
$426$		0			0
$427$	−0.923240	+	8.78404i	−0.0446787	+	0.425090i
$428$	−32.4052	−	56.1274i	−1.56636	−	2.71302i
$429$		0			0
$430$	−3.97845	−	2.89052i	−0.191858	−	0.139393i
$431$	−2.66850	+	2.96367i	−0.128537	+	0.142755i	−0.803978	−	0.594660i	$-0.797287\pi$
$431$	−2.66850	+	2.96367i	−0.128537	+	0.142755i	0.675441	+	0.737414i	$0.263954\pi$
$432$		0			0
$433$	18.0766			0.868704			0.434352	−	0.900743i	$-0.356977\pi$
$433$	18.0766			0.868704			0.434352	+	0.900743i	$0.356977\pi$
$434$	−25.6482	+	3.34513i	−1.23115	+	0.160571i
$435$		0			0
$436$	11.6673	−	35.9082i	0.558762	−	1.71969i
$437$	−0.926510	+	1.02899i	−0.0443210	+	0.0492234i
$438$		0			0
$439$	−11.4543	+	19.8394i	−0.546684	+	0.946884i	0.451815	+	0.892112i	$0.350777\pi$
$439$	−11.4543	+	19.8394i	−0.546684	+	0.946884i	−0.998499	+	0.0547723i	$0.982557\pi$
$440$	3.54257	+	6.13591i	0.168885	+	0.292518i
$441$		0			0
$442$	−22.0715	+	16.0359i	−1.04984	+	0.762750i
$443$	−2.24645	−	21.3736i	−0.106732	−	1.01549i	−0.908509	−	0.417866i	$-0.862778\pi$
$443$	−2.24645	−	21.3736i	−0.106732	−	1.01549i	0.801777	−	0.597624i	$-0.203888\pi$
$444$		0			0
$445$	−8.51257	+	3.79004i	−0.403535	+	0.179665i
$446$	−24.7244	+	5.25533i	−1.17073	+	0.248847i
$447$		0			0
$448$	−33.0912	−	14.7331i	−1.56341	−	0.696075i
$449$	−5.80940	−	17.8795i	−0.274163	−	0.843786i	−0.989440	−	0.144945i	$-0.953700\pi$
$449$	−5.80940	−	17.8795i	−0.274163	−	0.843786i	0.715277	−	0.698841i	$-0.246300\pi$
$450$		0			0
$451$	0.127127	+	0.0566007i	0.00598619	+	0.00266522i
$452$	85.4012	+	18.1526i	4.01694	+	0.853826i
$453$		0			0
$454$	−20.7897	+	9.25617i	−0.975709	+	0.434414i
$455$	2.58045	+	2.86588i	0.120973	+	0.134354i
$456$		0			0
$457$	−3.32182	+	2.41344i	−0.155388	+	0.112896i	−0.662763	−	0.748830i	$-0.730616\pi$
$457$	−3.32182	+	2.41344i	−0.155388	+	0.112896i	0.507374	+	0.861726i	$0.330616\pi$
$458$	−6.42352	+	61.1158i	−0.300152	+	2.85575i
$459$		0			0
$460$	0.859060	−	1.48794i	0.0400539	−	0.0693754i
$461$	−18.5063	−	13.4456i	−0.861924	−	0.626225i	0.0664836	−	0.997788i	$-0.478822\pi$
$461$	−18.5063	−	13.4456i	−0.861924	−	0.626225i	−0.928408	+	0.371563i	$0.878822\pi$
$462$		0			0
$463$	−5.11947	+	15.7561i	−0.237922	+	0.732249i	0.758798	+	0.651326i	$0.225787\pi$
$463$	−5.11947	+	15.7561i	−0.237922	+	0.732249i	−0.996720	+	0.0809233i	$0.974213\pi$
$464$	105.308			4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	−11.7878	+	36.2792i	−0.545476	+	1.67880i	0.174379	+	0.984679i	$0.444208\pi$
$467$	−11.7878	+	36.2792i	−0.545476	+	1.67880i	−0.719855	+	0.694124i	$0.755792\pi$
$468$		0			0
$469$	11.5936	+	8.42323i	0.535342	+	0.388949i
$470$	5.50321	−	9.53184i	0.253844	−	0.439671i
$471$		0			0
$472$	0.424374	−	4.03765i	0.0195334	−	0.185848i
$473$	3.25101	−	2.36200i	0.149482	−	0.108605i
$474$		0			0
$475$	7.95463	+	8.83451i	0.364984	+	0.405355i
$476$	−22.8256	+	10.1626i	−1.04621	+	0.465802i
$477$		0			0
$478$	48.0830	+	10.2204i	2.19926	+	0.467468i
$479$	30.7726	+	13.7008i	1.40603	+	0.626007i	0.962755	−	0.270377i	$-0.0871483\pi$
$479$	30.7726	+	13.7008i	1.40603	+	0.626007i	0.443279	+	0.896383i	$0.353815\pi$
$480$		0			0
$481$	8.78511	+	27.0378i	0.400567	+	1.23282i
$482$	−44.6580	−	19.8830i	−2.03412	−	0.905647i
$483$		0			0
$484$	47.1853	−	10.0295i	2.14479	−	0.455888i
$485$	0.710949	−	0.316535i	0.0322825	−	0.0143731i
$486$		0			0
$487$	2.16130	+	20.5634i	0.0979379	+	0.931817i	0.927606	+	0.373560i	$0.121863\pi$
$487$	2.16130	+	20.5634i	0.0979379	+	0.931817i	−0.829668	+	0.558257i	$0.811470\pi$
$488$	36.0319	−	26.1787i	1.63109	−	1.18506i
$489$		0			0
$490$	−3.28793	−	5.69487i	−0.148534	−	0.257268i
$491$	12.3664	−	21.4192i	0.558087	−	0.966634i	−0.439570	−	0.898209i	$-0.644869\pi$
$491$	12.3664	−	21.4192i	0.558087	−	0.966634i	0.997656	−	0.0684258i	$-0.0217976\pi$
$492$		0			0
$493$	15.0314	−	16.6941i	0.676982	−	0.751864i
$494$	−7.83511	+	24.1140i	−0.352518	+	1.08494i
$495$		0			0
$496$	54.7775	+	46.8990i	2.45958	+	2.10583i
$497$	8.21771			0.368615
$498$		0			0
$499$	−16.4340	+	18.2518i	−0.735685	+	0.817061i	−0.988622	−	0.150422i	$-0.951937\pi$
$499$	−16.4340	+	18.2518i	−0.735685	+	0.817061i	0.252937	+	0.967483i	$0.418604\pi$
$500$	−24.8218	−	18.0341i	−1.11006	−	0.806509i
$501$		0			0
$502$	−30.8429	−	53.4215i	−1.37659	−	2.38432i
$503$	1.54066	−	14.6584i	0.0686946	−	0.653585i	−0.904951	−	0.425517i	$-0.860092\pi$
$503$	1.54066	−	14.6584i	0.0686946	−	0.653585i	0.973645	−	0.228068i	$-0.0732410\pi$
$504$		0			0
$505$	−0.516394	−	4.91316i	−0.0229792	−	0.218633i
$506$	1.29821	+	1.44181i	0.0577126	+	0.0640963i
$507$		0			0
$508$	66.1285	−	14.0561i	2.93398	−	0.623637i
$509$	15.1674	+	3.22394i	0.672285	+	0.142899i	0.531392	−	0.847126i	$-0.321669\pi$
$509$	15.1674	+	3.22394i	0.672285	+	0.142899i	0.140893	+	0.990025i	$0.455003\pi$
$510$		0			0
$511$	−4.00557	−	12.3279i	−0.177196	−	0.545353i
$512$	0.0418393	+	0.128768i	0.00184905	+	0.00569080i
$513$		0			0
$514$	0.279433	+	0.0593953i	0.0123253	+	0.00261982i
$515$	9.01709	−	1.91664i	0.397341	−	0.0844574i
$516$		0			0
$517$	6.01812	+	6.68380i	0.264677	+	0.293953i
$518$	3.76092	+	35.7828i	0.165245	+	1.57220i
$519$		0			0
$520$	2.03268	−	19.3396i	0.0891388	−	0.848099i
$521$	14.7073	+	25.4738i	0.644337	+	1.11603i	0.984454	+	0.175642i	$0.0562001\pi$
$521$	14.7073	+	25.4738i	0.644337	+	1.11603i	−0.340117	+	0.940383i	$0.610467\pi$
$522$		0			0
$523$	−36.4268	−	26.4656i	−1.59283	−	1.15726i	−0.899754	−	0.436397i	$-0.856254\pi$
$523$	−36.4268	−	26.4656i	−1.59283	−	1.15726i	−0.693078	−	0.720863i	$-0.743746\pi$
$524$	8.54247	−	9.48737i	0.373180	−	0.414458i
$525$		0			0
$526$	19.6309			0.855947
$527$	15.2535	−	1.98942i	0.664455	−	0.0866604i
$528$		0			0
$529$	−7.01753	+	21.5977i	−0.305110	+	0.939032i
$530$	3.06499	−	3.40402i	0.133135	−	0.147861i
$531$		0			0
$532$	−11.6105	+	20.1099i	−0.503378	+	0.871876i
$533$	−0.190970	−	0.330769i	−0.00827182	−	0.0143272i
$534$		0			0
$535$	6.09119	−	4.42551i	0.263345	−	0.191331i
$536$	−7.55343	−	71.8661i	−0.326258	−	3.10414i
$537$		0			0
$538$	−39.8604	+	17.7470i	−1.71850	+	0.765127i
$539$	5.25607	−	1.11721i	0.226395	−	0.0481217i
$540$		0			0
$541$	34.5126	+	15.3660i	1.48381	+	0.660635i	0.979234	−	0.202731i	$-0.0649818\pi$
$541$	34.5126	+	15.3660i	1.48381	+	0.660635i	0.504577	+	0.863367i	$0.331648\pi$
$542$	−4.27759	−	13.1651i	−0.183738	−	0.565488i
$543$		0			0
$544$	43.9830	+	19.5825i	1.88576	+	0.839593i
$545$	4.29034	+	0.911941i	0.183778	+	0.0390632i
$546$		0			0
$547$	−16.6345	+	7.40617i	−0.711241	+	0.316665i	−0.730274	−	0.683154i	$-0.760608\pi$
$547$	−16.6345	+	7.40617i	−0.711241	+	0.316665i	0.0190333	+	0.999819i	$0.493941\pi$
$548$	−28.5375	−	31.6942i	−1.21906	−	1.35391i
$549$		0			0
$550$	13.4761	−	9.79092i	0.574621	−	0.417486i
$551$	2.18229	−	20.7631i	0.0929686	−	0.884537i
$552$		0			0
$553$	−8.37446	+	14.5050i	−0.356118	+	0.616815i
$554$	36.8305	+	26.7590i	1.56478	+	1.13688i
$555$		0			0
$556$	−2.19015	+	6.74059i	−0.0928831	+	0.285865i
$557$	9.19760			0.389715			0.194857	−	0.980832i	$-0.437576\pi$
$557$	9.19760			0.389715			0.194857	+	0.980832i	$0.437576\pi$
$558$		0			0
$559$	−11.0293			−0.466488
$560$	4.20481	−	12.9411i	0.177686	−	0.546860i
$561$		0			0
$562$	4.14964	+	3.01489i	0.175042	+	0.127175i
$563$	−18.0809	+	31.3170i	−0.762019	+	1.31986i	0.179790	+	0.983705i	$0.442458\pi$
$563$	−18.0809	+	31.3170i	−0.762019	+	1.31986i	−0.941808	+	0.336150i	$0.890875\pi$
$564$		0			0
$565$	−1.06022	+	10.0873i	−0.0446037	+	0.424375i
$566$	33.3200	−	24.2084i	1.40054	−	1.01755i
$567$		0			0
$568$	−27.7276	−	30.7946i	−1.16342	−	1.29211i
$569$	−37.9119	+	16.8795i	−1.58935	+	0.707624i	−0.995303	−	0.0968056i	$-0.969137\pi$
$569$	−37.9119	+	16.8795i	−1.58935	+	0.707624i	−0.594047	+	0.804430i	$0.702471\pi$
$570$		0			0
$571$	31.6853	+	6.73491i	1.32599	+	0.281847i	0.815859	−	0.578251i	$-0.196265\pi$
$571$	31.6853	+	6.73491i	1.32599	+	0.281847i	0.510128	+	0.860099i	$0.329598\pi$
$572$	23.4861	+	10.4567i	0.982004	+	0.437216i
$573$		0			0
$574$	−0.149373	−	0.459722i	−0.00623470	−	0.0191884i
$575$	−2.28085	−	1.01550i	−0.0951182	−	0.0423494i
$576$		0			0
$577$	−40.0870	+	8.52075i	−1.66884	+	0.354723i	−0.942911	−	0.333044i	$-0.891924\pi$
$577$	−40.0870	+	8.52075i	−1.66884	+	0.354723i	−0.725931	+	0.687768i	$0.758591\pi$
$578$	−23.0197	+	10.2490i	−0.957494	+	0.426304i
$579$		0			0
$580$	2.70786	+	25.7636i	0.112438	+	1.06977i
$581$	23.3096	−	16.9354i	0.967046	−	0.702600i
$582$		0			0
$583$	1.87151	+	3.24155i	0.0775100	+	0.134251i
$584$	−32.6814	+	56.6059i	−1.35237	+	2.34237i
$585$		0			0
$586$	−48.2304	+	53.5652i	−1.99238	+	2.21276i
$587$	−7.88963	+	24.2818i	−0.325640	+	1.00222i	0.645511	+	0.763751i	$0.276644\pi$
$587$	−7.88963	+	24.2818i	−0.325640	+	1.00222i	−0.971151	+	0.238466i	$0.923356\pi$
$588$		0			0
$589$	10.3820	−	9.82833i	0.427783	−	0.404969i
$590$	0.763058			0.0314146
$591$		0			0
$592$	67.1206	−	74.5449i	2.75864	−	3.06378i
$593$	36.0269	+	26.1751i	1.47945	+	1.07488i	0.977734	+	0.209850i	$0.0672976\pi$
$593$	36.0269	+	26.1751i	1.47945	+	1.07488i	0.501716	+	0.865033i	$0.332702\pi$
$594$		0			0
$595$	−1.45132	−	2.51375i	−0.0594982	−	0.103054i
$596$	−4.92879	+	46.8943i	−0.201891	+	1.92086i
$597$		0			0
$598$	−0.556616	−	5.29584i	−0.0227617	−	0.216563i
$599$	−12.7001	−	14.1049i	−0.518911	−	0.576309i	0.425549	−	0.904935i	$-0.360081\pi$
$599$	−12.7001	−	14.1049i	−0.518911	−	0.576309i	−0.944460	+	0.328627i	$0.893414\pi$
$600$		0			0
$601$	12.5592	−	2.66955i	0.512301	−	0.108893i	0.0554947	−	0.998459i	$-0.482326\pi$
$601$	12.5592	−	2.66955i	0.512301	−	0.108893i	0.456807	+	0.889566i	$0.348993\pi$
$602$	−13.6535	−	2.90215i	−0.556477	−	0.118283i
$603$		0			0
$604$	−5.19217	−	15.9799i	−0.211267	−	0.650212i
$605$	1.73175	+	5.32977i	0.0704056	+	0.216686i
$606$		0			0
$607$	37.3059	+	7.92960i	1.51420	+	0.321853i	0.888742	−	0.458407i	$-0.151580\pi$
$607$	37.3059	+	7.92960i	1.51420	+	0.321853i	0.625456	+	0.780260i	$0.284913\pi$
$608$	43.7670	−	9.30297i	1.77499	−	0.377285i
$609$		0			0
$610$	5.60124	+	6.22081i	0.226788	+	0.251873i
$611$	−2.58030	−	24.5499i	−0.104388	−	0.993184i
$612$		0			0
$613$	1.93821	−	18.4408i	0.0782834	−	0.744817i	−0.883022	−	0.469332i	$-0.844495\pi$
$613$	1.93821	−	18.4408i	0.0782834	−	0.744817i	0.961305	−	0.275485i	$-0.0888385\pi$
$614$	−12.0401	−	20.8541i	−0.485901	−	0.841605i
$615$		0			0
$616$	16.2701	+	11.8209i	0.655541	+	0.476278i
$617$	−5.44374	+	6.04589i	−0.219157	+	0.243398i	−0.842691	−	0.538398i	$-0.819030\pi$
$617$	−5.44374	+	6.04589i	−0.219157	+	0.243398i	0.623534	+	0.781796i	$0.285696\pi$
$618$		0			0
$619$	−5.36063			−0.215462			−0.107731	−	0.994180i	$-0.534359\pi$
$619$	−5.36063			−0.215462			−0.107731	+	0.994180i	$0.534359\pi$
$620$	−10.0653	+	14.6072i	−0.404232	+	0.586641i
$621$		0			0
$622$	−17.1711	+	52.8472i	−0.688499	+	2.11898i
$623$	−17.6981	+	19.6557i	−0.709058	+	0.787489i
$624$		0			0
$625$	−9.79252	+	16.9611i	−0.391701	+	0.678446i
$626$	−0.607062	−	1.05146i	−0.0242631	−	0.0420249i
$627$		0			0
$628$	14.0948	−	10.2404i	0.562442	−	0.408638i
$629$	−2.23670	−	21.2808i	−0.0891830	−	0.848519i
$630$		0			0
$631$	26.5358	−	11.8145i	1.05637	−	0.470327i	0.196324	−	0.980539i	$-0.437100\pi$
$631$	26.5358	−	11.8145i	1.05637	−	0.470327i	0.860049	+	0.510212i	$0.170433\pi$
$632$	82.6116	−	17.5596i	3.28611	−	0.698485i
$633$		0			0
$634$	13.7154	+	6.10647i	0.544707	+	0.242519i
$635$	2.42699	+	7.46949i	0.0963120	+	0.296418i
$636$		0			0
$637$	−13.4733	−	5.99868i	−0.533830	−	0.237677i
$638$	−28.6139	−	6.08208i	−1.13284	−	0.240792i
$639$		0			0
$640$	−11.9916	+	5.33902i	−0.474011	+	0.211043i
$641$	18.4717	+	20.5149i	0.729589	+	0.810290i	0.987788	−	0.155801i	$-0.0497959\pi$
$641$	18.4717	+	20.5149i	0.729589	+	0.810290i	−0.258200	+	0.966092i	$0.583129\pi$
$642$		0			0
$643$	3.42136	−	2.48577i	0.134925	−	0.0980291i	−0.518275	−	0.855214i	$-0.673426\pi$
$643$	3.42136	−	2.48577i	0.134925	−	0.0980291i	0.653201	+	0.757185i	$0.273426\pi$
$644$	0.509768	−	4.85012i	0.0200877	−	0.191121i
$645$		0			0
$646$	9.54202	−	16.5273i	0.375426	−	0.650257i
$647$	−21.2617	−	15.4475i	−0.835883	−	0.607304i	0.0853349	−	0.996352i	$-0.472804\pi$
$647$	−21.2617	−	15.4475i	−0.835883	−	0.607304i	−0.921217	+	0.389048i	$0.872804\pi$
$648$		0			0
$649$	−0.192683	+	0.593018i	−0.00756348	+	0.0232780i
$650$	−45.7184			−1.79322
$651$		0			0
$652$	9.11408			0.356935
$653$	4.12592	−	12.6983i	0.161460	−	0.496922i	−0.837298	−	0.546746i	$-0.815866\pi$
$653$	4.12592	−	12.6983i	0.161460	−	0.496922i	0.998758	+	0.0498246i	$0.0158662\pi$
$654$		0			0
$655$	1.19986	+	0.871749i	0.0468824	+	0.0340621i
$656$	−0.673821	+	1.16709i	−0.0263083	+	0.0455673i
$657$		0			0
$658$	3.26561	−	31.0702i	0.127307	−	1.21124i
$659$	−12.4717	+	9.06119i	−0.485827	+	0.352974i	−0.803577	−	0.595200i	$-0.797073\pi$
$659$	−12.4717	+	9.06119i	−0.485827	+	0.352974i	0.317750	+	0.948174i	$0.397073\pi$
$660$		0			0
$661$	−3.16035	−	3.50992i	−0.122923	−	0.136520i	0.678542	−	0.734562i	$-0.262612\pi$
$661$	−3.16035	−	3.50992i	−0.122923	−	0.136520i	−0.801465	+	0.598042i	$0.795946\pi$
$662$	59.4868	−	26.4852i	2.31202	−	1.02938i
$663$		0			0
$664$	−142.112	−	30.2069i	−5.51502	−	1.17225i
$665$	−2.46439	−	1.09722i	−0.0955651	−	0.0425483i
$666$		0			0
$667$	1.35493	+	4.17006i	0.0524632	+	0.161465i
$668$	67.0573	+	29.8558i	2.59453	+	1.15516i
$669$		0			0
$670$	13.2849	−	2.82379i	0.513239	−	0.109092i
$671$	−6.24895	+	2.78221i	−0.241238	+	0.107406i
$672$		0			0
$673$	3.24801	+	30.9028i	0.125202	+	1.19121i	0.859046	+	0.511898i	$0.171057\pi$
$673$	3.24801	+	30.9028i	0.125202	+	1.19121i	−0.733845	+	0.679317i	$0.762276\pi$
$674$	−24.0185	+	17.4505i	−0.925158	+	0.672167i
$675$		0			0
$676$	−1.24058	−	2.14875i	−0.0477147	−	0.0826443i
$677$	−4.51998	+	7.82883i	−0.173717	+	0.300886i	−0.939716	−	0.341955i	$-0.888911\pi$
$677$	−4.51998	+	7.82883i	−0.173717	+	0.300886i	0.766000	+	0.642841i	$0.222244\pi$
$678$		0			0
$679$	1.47810	−	1.64159i	0.0567242	−	0.0629986i
$680$	−4.52297	+	13.9203i	−0.173448	+	0.533818i
$681$		0			0
$682$	−12.1753	−	15.9069i	−0.466216	−	0.609107i
$683$	−7.13535			−0.273027			−0.136513	−	0.990638i	$-0.543590\pi$
$683$	−7.13535			−0.273027			−0.136513	+	0.990638i	$0.543590\pi$
$684$		0			0
$685$	3.31525	−	3.68196i	0.126669	−	0.140681i
$686$	−41.4091	−	30.0854i	−1.58101	−	1.14867i
$687$		0			0
$688$	19.4579	+	33.7021i	0.741826	+	1.28488i
$689$	1.07385	−	10.2170i	0.0409103	−	0.389236i
$690$		0			0
$691$	−3.81272	−	36.2756i	−0.145043	−	1.37999i	−0.788749	−	0.614716i	$-0.789271\pi$
$691$	−3.81272	−	36.2756i	−0.145043	−	1.37999i	0.643706	−	0.765273i	$-0.277396\pi$
$692$	0.0419833	+	0.0466272i	0.00159597	+	0.00177250i
$693$		0			0
$694$	−48.8576	+	10.3850i	−1.85461	+	0.394210i
$695$	−0.805371	−	0.171187i	−0.0305495	−	0.00649349i
$696$		0			0
$697$	0.0888351	+	0.273406i	0.00336487	+	0.0103560i
$698$	−26.7469	−	82.3185i	−1.01238	−	3.11580i
$699$		0			0
$700$	−40.9555	−	8.70536i	−1.54797	−	0.329032i
$701$	−1.57916	+	0.335661i	−0.0596441	+	0.0126777i	−0.237637	−	0.971354i	$-0.576373\pi$
$701$	−1.57916	+	0.335661i	−0.0596441	+	0.0126777i	0.177993	+	0.984032i	$0.443040\pi$
$702$		0			0
$703$	−13.3067	−	14.7786i	−0.501873	−	0.557386i
$704$	−2.93233	−	27.8993i	−0.110516	−	1.05149i
$705$		0			0
$706$	9.05833	−	86.1843i	0.340915	−	3.24359i
$707$	−7.01134	−	12.1440i	−0.263688	−	0.456722i
$708$		0			0
$709$	−9.29395	−	6.75245i	−0.349042	−	0.253594i	0.399425	−	0.916766i	$-0.369210\pi$
$709$	−9.29395	−	6.75245i	−0.349042	−	0.253594i	−0.748467	+	0.663172i	$0.769210\pi$
$710$	5.21141	−	5.78785i	0.195581	−	0.217214i
$711$		0			0
$712$	133.372			4.99833
$713$	−1.15235	+	2.77254i	−0.0431558	+	0.103832i
$714$		0			0
$715$	−0.922919	+	2.84045i	−0.0345152	+	0.106227i
$716$	34.9649	−	38.8324i	1.30670	−	1.45124i
$717$		0			0
$718$	28.4649	−	49.3026i	1.06230	−	1.83996i
$719$	−7.08549	−	12.2724i	−0.264244	−	0.457685i	0.703121	−	0.711070i	$-0.251789\pi$
$719$	−7.08549	−	12.2724i	−0.264244	−	0.457685i	−0.967365	+	0.253386i	$0.918456\pi$
$720$		0			0
$721$	21.1692	−	15.3803i	0.788382	−	0.572793i
$722$	3.48883	+	33.1940i	0.129841	+	1.23535i
$723$		0			0
$724$	−89.0009	+	39.6258i	−3.30769	+	1.47268i
$725$	36.8222	−	7.82681i	1.36754	−	0.290680i
$726$		0			0
$727$	−24.6180	−	10.9606i	−0.913030	−	0.406507i	−0.104205	−	0.994556i	$-0.533230\pi$
$727$	−24.6180	−	10.9606i	−0.913030	−	0.406507i	−0.808826	+	0.588049i	$0.799896\pi$
$728$	−17.0569	−	52.4958i	−0.632172	−	1.94562i
$729$		0			0
$730$	−11.2229	−	4.99675i	−0.415378	−	0.184938i
$731$	8.12005	+	1.72597i	0.300331	+	0.0638373i
$732$		0			0
$733$	−25.9662	+	11.5609i	−0.959083	+	0.427011i	−0.825735	−	0.564058i	$-0.809239\pi$
$733$	−25.9662	+	11.5609i	−0.959083	+	0.427011i	−0.133348	+	0.991069i	$0.542573\pi$
$734$	23.3944	+	25.9822i	0.863504	+	0.959019i
$735$		0			0
$736$	−7.60254	+	5.52357i	−0.280233	+	0.203601i
$737$	−1.16009	+	11.0375i	−0.0427324	+	0.406572i
$738$		0			0
$739$	0.348653	−	0.603885i	0.0128254	−	0.0222143i	−0.859541	−	0.511066i	$-0.829251\pi$
$739$	0.348653	−	0.603885i	0.0128254	−	0.0222143i	0.872367	+	0.488852i	$0.162584\pi$
$740$	19.9633	+	14.5042i	0.733866	+	0.533185i
$741$		0			0
$742$	4.01777	−	12.3654i	0.147497	−	0.453949i
$743$	18.1815			0.667015			0.333508	−	0.942747i	$-0.391768\pi$
$743$	18.1815			0.667015			0.333508	+	0.942747i	$0.391768\pi$
$744$		0			0
$745$	−5.47779			−0.200691
$746$	−3.67929	+	11.3237i	−0.134708	+	0.414589i
$747$		0			0
$748$	−15.6548	−	11.3738i	−0.572395	−	0.415869i
$749$	10.6856	−	18.5080i	0.390443	−	0.676267i
$750$		0			0
$751$	3.87445	−	36.8629i	0.141381	−	1.34515i	−0.661920	−	0.749574i	$-0.730258\pi$
$751$	3.87445	−	36.8629i	0.141381	−	1.34515i	0.803301	−	0.595573i	$-0.203075\pi$
$752$	−70.4650	+	51.1958i	−2.56959	+	1.86692i
$753$		0			0
$754$	53.7242	+	59.6668i	1.95652	+	2.17294i
$755$	1.78319	−	0.793927i	0.0648969	−	0.0288940i
$756$		0			0
$757$	−6.26211	−	1.33105i	−0.227600	−	0.0483779i	0.0926997	−	0.995694i	$-0.470450\pi$
$757$	−6.26211	−	1.33105i	−0.227600	−	0.0483779i	−0.320300	+	0.947316i	$0.603784\pi$
$758$	−36.7549	−	16.3643i	−1.33500	−	0.594380i
$759$		0			0
$760$	4.20351	+	12.9371i	0.152477	+	0.469277i
$761$	19.4940	+	8.67928i	0.706657	+	0.314624i	0.728412	−	0.685140i	$-0.240259\pi$
$761$	19.4940	+	8.67928i	0.706657	+	0.314624i	−0.0217552	+	0.999763i	$0.506925\pi$
$762$		0			0
$763$	12.1780	−	2.58852i	0.440874	−	0.0937106i
$764$	−5.73201	+	2.55206i	−0.207377	+	0.0923302i
$765$		0			0
$766$	−3.27605	−	31.1696i	−0.118369	−	1.12620i
$767$	1.38454	−	1.00593i	0.0499928	−	0.0363219i
$768$		0			0
$769$	6.12828	+	10.6145i	0.220991	+	0.382768i	0.955109	−	0.296254i	$-0.0957374\pi$
$769$	6.12828	+	10.6145i	0.220991	+	0.382768i	−0.734118	+	0.679022i	$0.762404\pi$
$770$	−1.88993	+	3.27346i	−0.0681084	+	0.117967i
$771$		0			0
$772$	44.5963	−	49.5292i	1.60506	−	1.78260i
$773$	10.7240	−	33.0050i	0.385714	−	1.18711i	−0.550247	−	0.835002i	$-0.685466\pi$
$773$	10.7240	−	33.0050i	0.385714	−	1.18711i	0.935961	−	0.352104i	$-0.114534\pi$
$774$		0			0
$775$	22.6393	+	12.3276i	0.813227	+	0.442820i
$776$	−11.1389			−0.399863
$777$		0			0
$778$	−25.9244	+	28.7920i	−0.929435	+	1.03224i
$779$	0.216146	+	0.157040i	0.00774425	+	0.00562652i
$780$		0			0
$781$	3.18213	+	5.51161i	0.113866	+	0.197221i
$782$	−0.418951	+	3.98605i	−0.0149817	+	0.142541i
$783$		0			0
$784$	5.43948	+	51.7532i	0.194267	+	1.84833i
$785$	1.35429	+	1.50409i	0.0483366	+	0.0536833i
$786$		0			0
$787$	19.6786	−	4.18281i	0.701465	−	0.149101i	0.156646	−	0.987655i	$-0.449932\pi$
$787$	19.6786	−	4.18281i	0.701465	−	0.149101i	0.544819	+	0.838554i	$0.316598\pi$
$788$	−15.2066	−	3.23227i	−0.541714	−	0.115145i
$789$		0			0
$790$	4.90526	+	15.0968i	0.174521	+	0.537122i
$791$	8.89666	+	27.3811i	0.316329	+	0.973559i
$792$		0			0
$793$	18.3640	+	3.90339i	0.652125	+	0.138613i
$794$	−41.5496	+	8.83165i	−1.47454	+	0.313423i
$795$		0			0
$796$	−46.1995	−	51.3097i	−1.63750	−	1.81863i
$797$	2.73885	+	26.0584i	0.0970150	+	0.923036i	0.929459	+	0.368926i	$0.120275\pi$
$797$	2.73885	+	26.0584i	0.0970150	+	0.923036i	−0.832444	+	0.554110i	$0.813059\pi$
$798$		0			0
$799$	−1.94213	+	18.4781i	−0.0687076	+	0.653709i
$800$	40.3405	+	69.8717i	1.42625	+	2.47034i
$801$		0			0
$802$	67.5183	+	49.0549i	2.38416	+	1.73219i
$803$	6.71722	−	7.46022i	0.237045	−	0.263266i
$804$		0			0
$805$	0.566550			0.0199683
$806$	1.37278	+	54.9626i	0.0483543	+	1.93598i
$807$		0			0
$808$	−21.8506	+	67.2491i	−0.768700	+	2.36582i
$809$	−24.3899	+	27.0877i	−0.857504	+	0.952354i	−0.999295	−	0.0375423i	$-0.988047\pi$
$809$	−24.3899	+	27.0877i	−0.857504	+	0.952354i	0.141791	+	0.989897i	$0.454714\pi$
$810$		0			0
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	−0.648114	−	0.761543i	$-0.724442\pi$
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	0.983573	+	0.180511i	$0.0577753\pi$
$812$	36.7660	+	63.6805i	1.29023	+	2.23475i
$813$		0			0
$814$	−22.5431	+	16.3785i	−0.790136	+	0.574067i
$815$	0.110675	+	1.05300i	0.00387676	+	0.0368849i
$816$		0			0
$817$	7.04810	−	3.13802i	0.246582	−	0.109785i
$818$	−17.3297	+	3.68355i	−0.605920	+	0.128792i
$819$		0			0
$820$	−0.302855	−	0.134840i	−0.0105762	−	0.00470881i
$821$	−12.1937	−	37.5285i	−0.425565	−	1.30975i	−0.902453	−	0.430789i	$-0.858235\pi$
$821$	−12.1937	−	37.5285i	−0.425565	−	1.30975i	0.476888	−	0.878964i	$-0.341765\pi$
$822$		0			0
$823$	−28.8571	−	12.8480i	−1.00589	−	0.447853i	−0.163401	−	0.986560i	$-0.552246\pi$
$823$	−28.8571	−	12.8480i	−1.00589	−	0.447853i	−0.842493	+	0.538707i	$0.818913\pi$
$824$	−129.063	−	27.4331i	−4.49611	−	0.955678i
$825$		0			0
$826$	1.97866	−	0.880958i	0.0688465	−	0.0306525i
$827$	−13.2688	−	14.7364i	−0.461400	−	0.512436i	0.466879	−	0.884321i	$-0.345378\pi$
$827$	−13.2688	−	14.7364i	−0.461400	−	0.512436i	−0.928279	+	0.371885i	$0.878712\pi$
$828$		0			0
$829$	−7.28104	+	5.28999i	−0.252881	+	0.183729i	−0.707003	−	0.707211i	$-0.749953\pi$
$829$	−7.28104	+	5.28999i	−0.252881	+	0.183729i	0.454122	+	0.890940i	$0.349953\pi$
$830$	2.85434	−	27.1572i	0.0990754	−	0.942640i
$831$		0			0
$832$	−38.4977	+	66.6800i	−1.33467	+	2.31171i
$833$	8.98066	+	6.52483i	0.311161	+	0.226072i
$834$		0			0
$835$	−2.63511	+	8.11003i	−0.0911917	+	0.280659i
$836$	−17.9836			−0.621976
$837$		0			0
$838$	39.4699			1.36347
$839$	9.84070	−	30.2866i	0.339739	−	1.04561i	−0.624602	−	0.780944i	$-0.714739\pi$
$839$	9.84070	−	30.2866i	0.339739	−	1.04561i	0.964340	−	0.264665i	$-0.0852614\pi$
$840$		0			0
$841$	−30.0234	−	21.8133i	−1.03529	−	0.752183i
$842$	35.9349	−	62.2411i	1.23840	−	2.14497i
$843$		0			0
$844$	−10.0353	+	95.4791i	−0.345428	+	3.28652i
$845$	0.233192	−	0.169424i	0.00802205	−	0.00582836i
$846$		0			0
$847$	10.6438	+	11.8212i	0.365726	+	0.406180i
$848$	−33.1145	+	14.7435i	−1.13716	+	0.506295i
$849$		0			0
$850$	33.6591	+	7.15447i	1.15450	+	0.245396i
$851$	3.81548	+	1.69876i	0.130793	+	0.0582328i
$852$		0			0
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	−0.775099	−	0.631839i	$-0.782300\pi$
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	0.255683	−	0.966761i	$-0.417700\pi$
$854$	21.7064	+	9.66431i	0.742778	+	0.330706i
$855$		0			0
$856$	−105.410	+	22.4056i	−3.60285	+	0.765809i
$857$	−17.5770	+	7.82580i	−0.600420	+	0.267324i	−0.684357	−	0.729147i	$-0.739917\pi$
$857$	−17.5770	+	7.82580i	−0.600420	+	0.267324i	0.0839371	+	0.996471i	$0.473251\pi$
$858$		0			0
$859$	−0.485236	−	4.61672i	−0.0165561	−	0.157520i	0.983120	−	0.182960i	$-0.0585680\pi$
$859$	−0.485236	−	4.61672i	−0.0165561	−	0.157520i	−0.999676	+	0.0254400i	$0.991901\pi$
$860$	−7.74487	+	5.62698i	−0.264098	+	0.191878i
$861$		0			0
$862$	5.36418	+	9.29104i	0.182705	+	0.316454i
$863$	−19.2652	+	33.3683i	−0.655795	+	1.13587i	0.325899	+	0.945405i	$0.394333\pi$
$863$	−19.2652	+	33.3683i	−0.655795	+	1.13587i	−0.981694	+	0.190466i	$0.939000\pi$
$864$		0			0
$865$	−0.00487728	+	0.00541676i	−0.000165832	+	0.000184175i
$866$	15.0271	−	46.2487i	0.510642	−	1.57159i
$867$		0			0
$868$	−9.23582	+	49.4981i	−0.313484	+	1.68008i
$869$	−12.9713			−0.440022
$870$		0			0
$871$	20.3823	−	22.6369i	0.690629	−	0.767021i
$872$	−50.7901	−	36.9012i	−1.71997	−	1.24963i
$873$		0			0
$874$	1.86246	+	3.22587i	0.0629986	+	0.109117i
$875$	1.05753	−	10.0618i	0.0357512	−	0.340150i
$876$		0			0
$877$	0.967760	+	9.20763i	0.0326789	+	0.310919i	0.998636	+	0.0522162i	$0.0166285\pi$
$877$	0.967760	+	9.20763i	0.0326789	+	0.310919i	−0.965957	+	0.258703i	$0.916705\pi$
$878$	41.2370	+	45.7983i	1.39168	+	1.54562i
$879$		0			0
$880$	10.3078	−	2.19099i	0.347475	−	0.0738582i
$881$	−17.4884	−	3.71727i	−0.589198	−	0.125238i	−0.0963414	−	0.995348i	$-0.530714\pi$
$881$	−17.4884	−	3.71727i	−0.589198	−	0.125238i	−0.492857	+	0.870110i	$0.664047\pi$
$882$		0			0
$883$	−14.9303	−	45.9509i	−0.502446	−	1.54637i	−0.805022	−	0.593244i	$-0.797847\pi$
$883$	−14.9303	−	45.9509i	−0.502446	−	1.54637i	0.302577	−	0.953125i	$-0.402153\pi$
$884$	16.4118	+	50.5104i	0.551990	+	1.69885i
$885$		0			0
$886$	−56.5516	−	12.0204i	−1.89989	−	0.403834i
$887$	22.9984	−	4.88847i	0.772211	−	0.164139i	0.195077	−	0.980788i	$-0.437504\pi$
$887$	22.9984	−	4.88847i	0.772211	−	0.164139i	0.577134	+	0.816649i	$0.304171\pi$
$888$		0			0
$889$	14.9170	+	16.5670i	0.500298	+	0.555638i
$890$	2.62025	+	24.9300i	0.0878310	+	0.835656i
$891$		0			0
$892$	−5.14346	+	48.9368i	−0.172216	+	1.63852i
$893$	8.63379	+	14.9542i	0.288919	+	0.500422i
$894$		0			0
$895$	4.91110	+	3.56812i	0.164160	+	0.119269i
$896$	−24.9312	+	27.6889i	−0.832894	+	0.925022i
$897$		0			0
$898$	−50.5739			−1.68767
$899$	−10.5150	−	44.0327i	−0.350696	−	1.46857i
$900$		0			0
$901$	−2.38945	+	7.35398i	−0.0796042	+	0.244996i
$902$	0.250494	−	0.278202i	0.00834053	−	0.00926310i
$903$		0			0
$904$	72.5879	−	125.726i	2.41424	−	4.18158i
$905$	−5.65893	−	9.80156i	−0.188109	−	0.325815i
$906$		0			0
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	−0.405821	−	0.913952i	$-0.633014\pi$
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	0.743815	+	0.668386i	$0.233014\pi$
$908$	4.63076	+	44.0588i	0.153677	+	1.46214i
$909$		0			0
$910$	9.47746	−	4.21964i	0.314175	−	0.139880i
$911$	−46.2512	+	9.83100i	−1.53237	+	0.325715i	−0.895432	−	0.445199i	$-0.853133\pi$
$911$	−46.2512	+	9.83100i	−1.53237	+	0.325715i	−0.636939	+	0.770914i	$0.719800\pi$
$912$		0			0
$913$	20.3847	+	9.07586i	0.674635	+	0.300367i
$914$	3.41333	+	10.5051i	0.112903	+	0.347479i
$915$		0			0
$916$	109.287	+	48.6578i	3.61095	+	1.60770i
$917$	4.11776	+	0.875258i	0.135981	+	0.0289036i
$918$		0			0
$919$	−21.1320	+	9.40858i	−0.697081	+	0.310360i	−0.724511	−	0.689263i	$-0.757934\pi$
$919$	−21.1320	+	9.40858i	−0.697081	+	0.310360i	0.0274300	+	0.999624i	$0.491268\pi$
$920$	−1.91161	−	2.12306i	−0.0630238	−	0.0699951i
$921$		0			0
$922$	−49.7848	+	36.1708i	−1.63958	+	1.19122i
$923$	1.82586	−	17.3719i	0.0600990	−	0.571804i
$924$		0			0
$925$	17.9291	−	31.0541i	0.589506	−	1.02105i
$926$	36.0560	+	26.1962i	1.18488	+	0.860862i
$927$		0			0
$928$	43.7846	−	134.755i	1.43730	−	4.42355i
$929$	−1.68694			−0.0553468			−0.0276734	−	0.999617i	$-0.508810\pi$
$929$	−1.68694			−0.0553468			−0.0276734	+	0.999617i	$0.508810\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	−26.3030	+	80.9524i	−0.861585	+	2.65169i
$933$		0			0
$934$	83.0208	+	60.3181i	2.71652	+	1.97367i
$935$	1.12398	−	1.94679i	0.0367581	−	0.0636669i
$936$		0			0
$937$	−2.06200	+	19.6186i	−0.0673625	+	0.640911i	0.907797	+	0.419409i	$0.137763\pi$
$937$	−2.06200	+	19.6186i	−0.0673625	+	0.640911i	−0.975160	+	0.221502i	$0.928904\pi$
$938$	31.1885	−	22.6598i	1.01834	−	0.739868i
$939$		0			0
$940$	−14.3370	−	15.9228i	−0.467620	−	0.519344i
$941$	8.06045	−	3.58874i	0.262763	−	0.116990i	−0.271127	−	0.962544i	$-0.587396\pi$
$941$	8.06045	−	3.58874i	0.262763	−	0.116990i	0.533890	+	0.845554i	$0.320730\pi$
$942$		0			0
$943$	−0.0548849	−	0.0116661i	−0.00178730	−	0.000379902i
$944$	−5.51642	−	2.45607i	−0.179544	−	0.0799382i
$945$		0			0
$946$	−3.34057	−	10.2812i	−0.108611	−	0.334271i
$947$	−14.2158	−	6.32930i	−0.461953	−	0.205675i	0.162545	−	0.986701i	$-0.448030\pi$
$947$	−14.2158	−	6.32930i	−0.461953	−	0.205675i	−0.624498	+	0.781026i	$0.714696\pi$
$948$		0			0
$949$	−26.9506	+	5.72853i	−0.874854	+	0.185956i
$950$	29.2157	−	13.0077i	0.947883	−	0.422025i
$951$		0			0
$952$	4.34271	+	41.3181i	0.140748	+	1.33913i
$953$	7.80840	−	5.67314i	0.252939	−	0.183771i	−0.454089	−	0.890956i	$-0.650035\pi$
$953$	7.80840	−	5.67314i	0.252939	−	0.183771i	0.707028	+	0.707185i	$0.250035\pi$
$954$		0			0
$955$	−0.364458	−	0.631260i	−0.0117936	−	0.0204271i
$956$	47.8473	−	82.8739i	1.54749	−	2.68033i
$957$		0			0
$958$	60.6348	−	67.3417i	1.95902	−	2.17571i
$959$	4.34583	−	13.3751i	0.140334	−	0.431904i
$960$		0			0
$961$	14.1404	−	27.5871i	0.456143	−	0.889907i
$962$	76.4790			2.46578
$963$		0			0
$964$	−63.6766	+	70.7201i	−2.05089	+	2.27774i
$965$	6.26392	+	4.55100i	0.201643	+	0.146502i
$966$		0			0
$967$	−14.1988	−	24.5930i	−0.456602	−	0.790858i	0.542177	−	0.840264i	$-0.317600\pi$
$967$	−14.1988	−	24.5930i	−0.456602	−	0.790858i	−0.998779	+	0.0494066i	$0.984267\pi$
$968$	8.38438	−	79.7720i	0.269484	−	2.56397i
$969$		0			0
$970$	−0.218837	−	2.08209i	−0.00702642	−	0.0668519i
$971$	14.8059	+	16.4436i	0.475144	+	0.527701i	0.932300	−	0.361686i	$-0.117799\pi$
$971$	14.8059	+	16.4436i	0.475144	+	0.527701i	−0.457156	+	0.889386i	$0.651132\pi$
$972$		0			0
$973$	−2.28602	+	0.485909i	−0.0732865	+	0.0155775i
$974$	54.4080	+	11.5648i	1.74334	+	0.370559i
$975$		0			0
$976$	−20.4703	−	63.0012i	−0.655240	−	2.01662i
$977$	6.15324	+	18.9377i	0.196859	+	0.605871i	0.999950	+	0.0100140i	$0.00318759\pi$
$977$	6.15324	+	18.9377i	0.196859	+	0.605871i	−0.803090	+	0.595857i	$0.796812\pi$
$978$		0			0
$979$	−20.0362	−	4.25884i	−0.640361	−	0.136113i
$980$	−12.5215	+	2.66153i	−0.399985	+	0.0850195i
$981$		0			0
$982$	−44.5206	−	49.4451i	−1.42071	−	1.57786i
$983$	−2.60593	−	24.7938i	−0.0831164	−	0.790800i	−0.954100	−	0.299488i	$-0.903184\pi$
$983$	−2.60593	−	24.7938i	−0.0831164	−	0.790800i	0.870984	−	0.491312i	$-0.163482\pi$
$984$		0			0
$985$	0.188783	−	1.79615i	0.00601513	−	0.0572302i
$986$	−30.2160	−	52.3356i	−0.962273	−	1.66671i
$987$		0			0
$988$	39.9319	+	29.0122i	1.27040	+	0.923002i
$989$	−1.08420	+	1.20413i	−0.0344757	+	0.0382891i
$990$		0			0
$991$	−42.0512			−1.33580			−0.667900	−	0.744251i	$-0.732807\pi$
$991$	−42.0512			−1.33580			−0.667900	+	0.744251i	$0.732807\pi$
$992$	82.7885	−	50.5953i	2.62854	−	1.60640i
$993$		0			0
$994$	6.83142	−	21.0249i	0.216679	−	0.666871i
$995$	5.36707	−	5.96074i	0.170148	−	0.188968i
$996$		0			0
$997$	−7.23233	+	12.5268i	−0.229050	+	0.396727i	−0.957527	−	0.288344i	$-0.906895\pi$
$997$	−7.23233	+	12.5268i	−0.229050	+	0.396727i	0.728477	+	0.685071i	$0.240229\pi$
$998$	33.0353	+	57.2189i	1.04572	+	1.81123i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.y.c.262.2		16
3.2	odd	2		31.2.g.a.14.1	✓	16
12.11	even	2		496.2.bg.c.417.1		16
15.2	even	4		775.2.ck.a.324.1		32
15.8	even	4		775.2.ck.a.324.4		32
15.14	odd	2		775.2.bl.a.76.2		16
31.12	odd	30		8649.2.a.be.1.8		8
31.19	even	15		8649.2.a.bf.1.8		8
31.20	even	15	inner	279.2.y.c.82.2		16
93.2	odd	10		961.2.c.j.521.1		16
93.5	odd	6		961.2.g.k.846.1		16
93.8	odd	10		961.2.g.t.338.2		16
93.11	even	30		961.2.g.l.547.1		16
93.14	odd	30		961.2.d.p.388.4		16
93.17	even	30		961.2.d.q.388.4		16
93.20	odd	30		31.2.g.a.20.1	yes	16
93.23	even	10		961.2.g.n.338.2		16
93.26	even	6		961.2.g.j.846.1		16
93.29	even	10		961.2.c.i.521.1		16
93.35	odd	10		961.2.g.k.844.1		16
93.38	odd	30		961.2.d.o.531.1		16
93.41	odd	30		961.2.c.j.439.1		16
93.44	even	30		961.2.g.n.816.2		16
93.47	odd	10		961.2.g.s.732.2		16
93.50	odd	30		961.2.a.i.1.1		8
93.53	even	30		961.2.g.m.235.2		16
93.56	odd	6		961.2.d.o.628.1		16
93.59	odd	30		961.2.d.p.374.4		16
93.65	even	30		961.2.d.q.374.4		16
93.68	even	6		961.2.d.n.628.1		16
93.71	odd	30		961.2.g.s.235.2		16
93.74	even	30		961.2.a.j.1.1		8
93.77	even	10		961.2.g.m.732.2		16
93.80	odd	30		961.2.g.t.816.2		16
93.83	even	30		961.2.c.i.439.1		16
93.86	even	30		961.2.d.n.531.1		16
93.89	even	10		961.2.g.j.844.1		16
93.92	even	2		961.2.g.l.448.1		16
372.299	even	30		496.2.bg.c.113.1		16
465.113	even	60		775.2.ck.a.299.1		32
465.299	odd	30		775.2.bl.a.51.2		16
465.392	even	60		775.2.ck.a.299.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	3.2	odd	2
31.2.g.a.20.1	yes	16	93.20	odd	30
279.2.y.c.82.2		16	31.20	even	15	inner
279.2.y.c.262.2		16	1.1	even	1	trivial
496.2.bg.c.113.1		16	372.299	even	30
496.2.bg.c.417.1		16	12.11	even	2
775.2.bl.a.51.2		16	465.299	odd	30
775.2.bl.a.76.2		16	15.14	odd	2
775.2.ck.a.299.1		32	465.113	even	60
775.2.ck.a.299.4		32	465.392	even	60
775.2.ck.a.324.1		32	15.2	even	4
775.2.ck.a.324.4		32	15.8	even	4
961.2.a.i.1.1		8	93.50	odd	30
961.2.a.j.1.1		8	93.74	even	30
961.2.c.i.439.1		16	93.83	even	30
961.2.c.i.521.1		16	93.29	even	10
961.2.c.j.439.1		16	93.41	odd	30
961.2.c.j.521.1		16	93.2	odd	10
961.2.d.n.531.1		16	93.86	even	30
961.2.d.n.628.1		16	93.68	even	6
961.2.d.o.531.1		16	93.38	odd	30
961.2.d.o.628.1		16	93.56	odd	6
961.2.d.p.374.4		16	93.59	odd	30
961.2.d.p.388.4		16	93.14	odd	30
961.2.d.q.374.4		16	93.65	even	30
961.2.d.q.388.4		16	93.17	even	30
961.2.g.j.844.1		16	93.89	even	10
961.2.g.j.846.1		16	93.26	even	6
961.2.g.k.844.1		16	93.35	odd	10
961.2.g.k.846.1		16	93.5	odd	6
961.2.g.l.448.1		16	93.92	even	2
961.2.g.l.547.1		16	93.11	even	30
961.2.g.m.235.2		16	93.53	even	30
961.2.g.m.732.2		16	93.77	even	10
961.2.g.n.338.2		16	93.23	even	10
961.2.g.n.816.2		16	93.44	even	30
961.2.g.s.235.2		16	93.71	odd	30
961.2.g.s.732.2		16	93.47	odd	10
961.2.g.t.338.2		16	93.8	odd	10
961.2.g.t.816.2		16	93.80	odd	30
8649.2.a.be.1.8		8	31.12	odd	30
8649.2.a.bf.1.8		8	31.19	even	15

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.831304 - 2.55849i) q^{2} +(-4.23677 - 3.07819i) q^{4} +(0.304192 - 0.526876i) q^{5} +(0.180508 - 1.71742i) q^{7} +(-7.04481 + 5.11835i) q^{8} +(-1.09513 - 1.21627i) q^{10} +(1.22177 - 0.543967i) q^{11} +(-3.59045 - 0.763174i) q^{13} +(-4.24394 - 1.88952i) q^{14} +(4.00227 + 12.3177i) q^{16} +(2.52396 + 1.12374i) q^{17} +(2.51157 - 0.533850i) q^{19} +(-2.91062 + 1.29589i) q^{20} +(-0.376072 - 3.57808i) q^{22} +(-0.436271 + 0.316969i) q^{23} +(2.31493 + 4.00958i) q^{25} +(-4.93733 + 8.55171i) q^{26} +(-6.05132 + 6.72067i) q^{28} +(2.51258 - 7.73291i) q^{29} +(4.75081 - 2.90341i) q^{31} +17.4262 q^{32} +(4.97326 - 5.52336i) q^{34} +(-0.849957 - 0.617530i) q^{35} +(-3.87249 - 6.70735i) q^{37} +(0.722025 - 6.86961i) q^{38} +(0.553763 + 5.26870i) q^{40} +(0.0696243 + 0.0773256i) q^{41} +(2.93904 - 0.624713i) q^{43} +(-6.85079 - 1.45618i) q^{44} +(0.448289 + 1.37969i) q^{46} +(2.07813 + 6.39584i) q^{47} +(3.93009 + 0.835366i) q^{49} +(12.1829 - 2.58955i) q^{50} +(12.8627 + 14.2855i) q^{52} +(0.292549 + 2.78341i) q^{53} +(0.0850494 - 0.809191i) q^{55} +(7.51871 + 13.0228i) q^{56} +(-17.6959 - 12.8568i) q^{58} +(-0.311970 + 0.346478i) q^{59} -5.11468 q^{61} +(-3.47898 - 14.5685i) q^{62} +(6.48190 - 19.9492i) q^{64} +(-1.49428 + 1.65957i) q^{65} +(-4.14923 + 7.18668i) q^{67} +(-7.23436 - 12.5303i) q^{68} +(-2.28652 + 1.66125i) q^{70} +(0.497420 + 4.73264i) q^{71} +(6.85725 - 3.05304i) q^{73} +(-20.3799 + 4.33188i) q^{74} +(-12.2842 - 5.46929i) q^{76} +(-0.713679 - 2.19648i) q^{77} +(-8.86044 - 3.94492i) q^{79} +(7.70738 + 1.63825i) q^{80} +(0.255716 - 0.113852i) q^{82} +(11.1642 + 12.3991i) q^{83} +(1.35984 - 0.987981i) q^{85} +(0.844916 - 8.03884i) q^{86} +(-5.82292 + 10.0856i) q^{88} +(-12.3911 - 9.00268i) q^{89} +(-1.95880 + 6.02855i) q^{91} +2.82407 q^{92} +18.0912 q^{94} +(0.482726 - 1.48568i) q^{95} +(1.03488 + 0.751881i) q^{97} +(5.40437 - 9.36065i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} - 14 q^{4} + 3 q^{5} + 2 q^{7} - 17 q^{8} - 2 q^{10} + 7 q^{11} - 7 q^{13} + 6 q^{14} - 2 q^{16} + 6 q^{17} + 16 q^{19} - 37 q^{20} + 9 q^{22} - q^{23} - 13 q^{25} - 9 q^{26} - 30 q^{28}+ \cdots + 10 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 14 * q^4 + 3 * q^5 + 2 * q^7 - 17 * q^8 - 2 * q^10 + 7 * q^11 - 7 * q^13 + 6 * q^14 - 2 * q^16 + 6 * q^17 + 16 * q^19 - 37 * q^20 + 9 * q^22 - q^23 - 13 * q^25 - 9 * q^26 - 30 * q^28 + 14 * q^29 + 15 * q^31 + 42 * q^32 - 32 * q^34 + 9 * q^35 - 8 * q^37 - 8 * q^38 - q^40 + 8 * q^41 + 23 * q^43 - 39 * q^44 + 34 * q^46 - 14 * q^47 + 2 * q^49 - 3 * q^50 + 29 * q^52 - 6 * q^53 - 7 * q^55 + 30 * q^56 - 15 * q^58 - 4 * q^59 - 60 * q^61 + 25 * q^62 + 23 * q^64 + 12 * q^65 + 13 * q^67 - 30 * q^68 + 12 * q^70 + 14 * q^71 + 2 * q^73 - 13 * q^74 - 12 * q^76 - 18 * q^77 + 18 * q^79 - 36 * q^80 + 14 * q^82 + 16 * q^83 + 37 * q^85 + 26 * q^86 - 17 * q^88 - q^89 + 8 * q^91 + 64 * q^92 + 44 * q^94 + 22 * q^95 + 3 * q^97 + 10 * q^98

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